The Micro and Macro of (Unconventional) Monetary Policy
Gregor Boehl
Uni Bonn
Motivation
Common shortcut:
central bank
sets
interest rate
Reality:
central bank
supplies
reserves & reserve rate
to
banks
banks
set
interest rate
Q: Banking sector important?
- For unconventional monetary policy: Yes!
- UMP potentially counterproductive
Data I
- Deposit & lending rates not directly controlled
- But rate central in macroeconomic theory: $\small c_t = E_t c_{t+1} - \frac{1}{\sigma} (\color{lightgreen}r_t \color{white}- E_t \pi_{t+1})$
- After 2009: No clear pass-through to deposit rate
Data II
- Reserves: funds of commercial banks stored at ECB
- Clearly policy driven (via asset purchases)
- No clear pass-through to HH deposits
This Paper
- Develop an IO-model of banking sector with liquidity friction
- Banks hold reserves to hedge liquidity risk
- Embedded into a medium-scale NK framework
- Mechanism:
Reserves up
liquidity
up
liquidity costs down
credit volume up lending rate down deposit rate ???
If credit demand very elastic:
credit volume
up²
lending rate
const.
deposit rate
up
aggregate demand falls!
credit volume up lending rate down deposit rate ???
If credit demand very elastic:
Policy Effectiveness
| reserves policy | ||
|---|---|---|
| MRR* binding | low | high |
| MRR* slack | high | low |
| sign of effect | state dependend: depends on supply of reserves |
state dependend: depends on investment elasticity |
Literature
- DSGE literature: Gertler & Karadi (2011,2013), Carstrom et al. (2013), Boehl et. al. (forthc.)
- Banking literature: Corbae & D'Erasmo (2021), Drechsler et al. (2017), Poole (1968)
- Monetary: Bianchi & Bigio (2022), Piazzesi et al. (2019)
Model:
An IO model of the banking sector
Banking sector: bank $i$'s problem
-
banks hold assets and reserves, backed by deposits:
$$ \definecolor{sgreen}{RGB}{78, 126, 100} \definecolor{sred}{RGB}{231, 75, 75} \definecolor{sblue}{RGB}{112, 174, 255} A_{i,t} + J_{i,t} = D_{i,t} \color{sgreen} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{white} + J_{i,t} = D_{i,t} \color{sgreen} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{white} + J_{i,t} = D_{i,t} \color{sblue} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- assets are fixed at the beginning of each period
- deposits subject to random transfers (prob. $\chi$)
- reserves $J_i > 0$ must compensate for $\Delta D_i$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$
Banking sector: bank $i$'s problem
$$
\small
\begin{align}
\text{Net outflow}& &\Delta {D}_{i} &\sim \mathcal{N} \left( 0, \frac{{D}_{i} D_{-i}}{\sum D_{j}} (2 \chi - \chi^2)\right)\\
\text{Exp. liquidity cost}& &g(J_{i}, D_{i}) &= E \Big[\Delta D_{i} - J_{i} | \Delta D_{i} > J_{i}\Big]
\end{align}
$$
Banking sector: bank $i$'s problem
- Expected cost for each bank: $$ g(J_{i,t}, D_{i,t}) = h(D_{i,t}) f_h\left(J_{i,t}\right) - J_{i,t} \left[1-F_h\left(J_{i,t}\right)\right], $$
- Banks are subject to a minimal reserve requirement (MRR) $$ \psi D_{i,t} \leq J_{i,t} $$
- Each bank $i$ maximizes profits s.t. balance sheet, expected costs, MRR & competitors actions
Banking sector: aggregation
FOCs:
$$
\small
\definecolor{sgreen}{RGB}{78, 126, 100}
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\color{sgreen}
\underbrace{
\color{white}
R^j -
R^b +
\gamma \left[1-
\hat{F}
\right]
}_{MPJ}
&=
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs:
$$
\small
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\underbrace{
R^j -
R^b +
\gamma \left[1-
\hat{F}
\right]
}_{MPJ}
&=
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs when MRR slack:
$$
\small
\begin{align}
R
= \color{sgreen}(1-\psi)\color{white} R^b \color{sgreen}+ \psi R^j
\color{white}
&-\gamma
\color{sgreen}
\left(
\color{white}
0.5\hat{f}
\color{sgreen}
-
\psi \left[1-\hat{F}\right]
\right)
\\
\color{white}
\underbrace{
R^j -
R^b +
\gamma \left[1-\hat{F}\right]
}_{MPJ}
&=
\color{sgreen}
\min\left\{
\color{white}
0
\color{sgreen},
\;
R^j -
R^b +
\gamma \left[1-\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs at MRR:
$$
\small
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\color{sgreen}
\underbrace{
R^j -
R^b +
\gamma \left[1-
\color{white}
\hat{F}
\color{sgreen}
\right]}_{MPJ}
&=
\color{sgreen}
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\color{white}
\hat{F}_\psi
\color{sgreen}
\right]
\right\}
\end{align}
$$
- IOR rate $R^j$, deposit rate $R$, lending rate $R^b$
- $\hat{f} = f\left(\hat{J}| 0, \hat{D}\right)$, $\hat{f}_\psi = f\left(\psi\hat{D}| 0, \hat{D}\right)$, $\hat{F}=...$
- Reserves & deposits scaled by liquidity risk $\hat{J} = \frac{J}{\nu}$
Banking sector: partial equilibrium
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \;\hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\gamma \left[1-
\hat{F}
\right]
\; &= \;
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\color{sgreen}
\gamma \left[1-
\color{white}
\hat{J}
\color{sgreen}
\right]
\; &= \;
\color{sgreen}
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\color{white}
\psi \hat{D}
\color{sgreen}
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\color{white}
\gamma \left[1-\hat{F}\right] \; &= \;
\color{sgreen}\min\left\{
\color{white}
R^b - R^j
\color{sgreen},
\;
\gamma \left[1-\hat{F}_\psi
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\gamma \left[1-
\hat{F}
\right]
\; &= \;
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
Banking sector: spreads
- Holding reserves & deposit constant
Results:
partial equilibrium
partial equilibrium: reserves policy
$$ \scriptsize \begin{align} R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\ \gamma \left[1- \hat{F} \right] &= \min\left\{ R^b - R^j, \; \gamma \left[1- \hat{F}_\psi \right] \right\} \end{align} $$
partial equilibrium: higher elasticity
$$
\scriptsize
\begin{align}
R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\gamma \left[1-
\hat{F}
\right]
&=
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
partial equilibrium: IOR policy
$$
\scriptsize
\begin{align}
R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\gamma \left[1-
\hat{F}
\right]
&=
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
Results:
general equilibrium
general equilibrium: model
- Embed banking sector into medium scale DSGE
-
Features:
capital, capital adjustment, capital utilization, sticky prices á la Rotemberg, debt financed transfers - Fact: determined under IOR & reserves peg (no Taylor principle)
-
Nonlinear perfect foresight solution (using econpizza
![]()
)
general equilibrium
reserves policy & the MRR
general equilibrium
reserves policy if MRR is slack
general equilibrium
reserves policy @ the MRR
general equilibrium
IOR policy: @ vs. slack MRR
Conclusion
-
Provide a unifying theory of the relationship of
- bank deposits
- central bank reserves
- minimal reserves requirements
- deposits, lending & reserves rate
- Effect of UMP is highly state dependent